Is it true that a heavier skier goes faster? If it is, why is that?
My intuition would be that the speed gained by a skier should be independent from its mass, since both its acceleration and the friction are proportional to its mass. Am I overlooking some important effect which would cause a heavier skier to go faster?
Answer
I'm quite sure that you've left something. The more their mass, they've got more momentum and of course, Inertia. The heavier the body is, the more their body resists their state of motion (or rest).
Yes. They move faster than skinny guys. If you resolve the forces acting on the skier like his acceleration, gravity, friction (of snow), the normal force and also his air drag, you can find that his velocity does depend on his mass.
Resolving all the forces, we get
$$ma=mg\ cos\theta-\mu\ mg\ sin\theta-\frac{1}{2}\rho Av^2C_d$$
$$a+\frac{1}{2m}\rho Av^2C_d=g\ cos\theta-\mu\ g\ sin\theta$$
As the mass is in the denominator portion, we can clearly see that it supports his acceleration (it should increase in order for balancing other forces) by opposing gravity.
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